Lights Out!

There are number of lights along a corridor. All of the lights are off. Each light has an on-off switch.
Several people walk along the corridor, one after another.

• The first flips every switch, turning them all on.
• The second flips every second switch, starting from the second, turning about half of them off.
• The third flips every third switch, starting from the third, turning some on and some off.
• The fourth flips every fourth switch, starting from the fourth.
• etc.

After all of the people have walked the corridor, how many switches are on?

Input

The input will be a two lines.
The first line contains $N$, the number of lights in the corridor.
The second line contains $M$, the number of people.

Output

Ouput the number of lights on after the M people have walked along the corridor.

Constraints

• $1 \le M \le N$
• $1 \le N \le 1,000$

Subtasks

• Subtask 1 (+30%): $M = 1$.
• Subtask 2 (+30%): $M \le 2$.
• Subtask 3 (+40%): No further constraints apply.